A priori error analysis for optimal distributed control problem governed by the first order linear hyperbolic equation: hp-streamline diffusion discontinuous galerkin method
A priori error analysis for optimal distributed control problem governed by the first order linear hyperbolic equation: hp-streamline diffusion discontinuous galerkin method
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DOI：
10.1515/jnma-2014-0049
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发表时间：
2016
影响因子：
3
通讯作者：
C. Xiong;Fusheng Luo;Xiuling Ma;Yuan Li
中科院分区：
文献类型：
--
作者：
C. Xiong;Fusheng Luo;Xiuling Ma;Yuan Li
摘要 在本文中，我们推导了一阶线性双曲方程控制的最优分布式控制问题的流线扩散DG有限元近似的先验误差分析（hp版本）。给出了该方法的稳定性，得到了状态和控制近似的先验误差上限，并证明了数值方法的收敛性。对于最优控制问题，这些估计显然在文献中不可用。
Abstract In the current paper, we derive the a priori error analysis (hp version) of the streamline diffusion DG finite element approximation for optimal distributed control problem governed by the first order linear hyperbolic equation. We present the stability of such method, obtain the a priori error upper bound for the state and the control approximation, and prove the convergence of numerical method. For the optimal control problem, these estimates are apparently not available in the literature.